Please also see examples under the ``problem'' directory and solve them by CF-induction.

(The desirable command is written in each example file, so, please try that command.)

3. How to write input files for the software

The input file mainly consists of three parts: the one is for representing the background theory,

the second is for representing examples, and the third is for representing the language bias.

3.1 Background theory B

Let C be a clause odd(X) ⊃ even(s(X)). Then C is written as follows:

cnf(c, bg, [-odd(X), even(X), successor(X, Y)]).

The first term ``c'' denotes the name of the clause C. We can write it arbitrarily.

The second term ``bg'' denotes that this clause is included in B. Note that any function symbol does not currently allowed due to the computational efficiency. Instead, we can add some new predicate which has the same meaning of the function.

Note also that our representation formalisms are not limited to Horn theories).

3.2 (Positive) Examples E

Let E be a clause odd(3). Then E is written as follows:

cnf(e, obs, [odd(3)]).

The first term ``e'' denotes the name of the clause E

The second term ``obs'' denotes that this clause is included in the positive examples.

Note here that if you need to treat some negative examples like -odd(2),

then it is enough to make them included in the background theory.

3.3 Language bias

Currently, we can use 3 types of the language bias in CF-induction as follows.